Koolen–Bang classification conjecture for geometric distance-regular graphs
Koolen–Bang classification conjecture for geometric distance-regular graphs
Let be a fixed integer. A geometric distance-regular graph has diameter and intersection number . Koolen–Bang's classification conjecture. Any geometric distance-regular graph with smallest eigenvalue is either a Johnson graph, a Grassmann graph, a Hamming graph, a bilinear forms graph, or has number of vertices bounded above by a function of . The source presents this as one of two conjectures proposed by Koolen and Bang; no resolution is given, so it remains open.
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Sources & referencesView supporting material
Primary source
Chenhui Lv and Jack H. Koolen, “On the characterization of geometric distance-regular graphs”, arXiv:2601.10330 (2026).
Additional references
2 papers in this index state this conjecture (2020–2026). The statement above is taken from the most recent of them; the others are arXiv:2011.11935.
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